Hi Senna!
I think the overflew tube where the fuel dropped out is the airbox-drainage.
When a float needle valve in the carburetor is broken, the fuel-level in the float chamber gets too high an it overflows into the airbox.
The fuel can also get into the cylinder and, past the piston ring, into the crankcase where it dilutes the oil - not good.
this would also explain your problems to start the engine again.
But all this can only happen, when the fuel cock (it's really named "cock"??
) is in "pri"-position or not functioning correctly.
Hope i could help you,
greetz
Pat